I actually have a PC doing this same exact thing now. Ordered New, came in fine, one month later *blam* it starts crashing without BSOD or anything. It just goes from straight on, to off.

I've narrowed my problem down to the CPU overheating (they used cheap grey grease which hardened like a rock), just waiting for a new air cooler to come in and I'll be good I think.

I'd recommend downloading a free system monitoring program like HWMonitor and just watch the temperatures as the system runs. If they start rising sharply from any activity, it could be that something in the system is overheating and causing an emergency shutdown. I can't say I've seen it do that for anything other than the CPU overheating though, other hardware usually throws up the BSOD for a few seconds.